Question

A 70 kg base runner begins his slide into second base when he is moving at a speed of 4 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. How much mechanical energy is lost due to friction acting on the runner? How far does he slide? An automobile having a mass of 1000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with a constant 5.00 times 10⁵ N/m and is compressed 3.06 cm as the car is brought to rest. What was the speed of the car before the impact assuming no energy is lost in the collision with the wall?

Answer 1

To calculate the distance a base runner slides, you need to find the work done by the friction force. The speed of the car before impact can be calculated using the principle of conservation of mechanical energy.

Step-by-step explanation:

To calculate the distance the base runner slides, we need to find the work done by the friction force, which is equal to the loss in mechanical energy. The work done by friction can be calculated using the formula:

Work = Force × Distance

The friction force can be found using the formula:

Force = Coefficient of Friction × Normal Force

And the normal force is equal to the weight of the runner, which is given by:

Normal Force = Mass × Gravity

Therefore, the distance the base runner slides can be calculated as:

Distance = Work ÷ Force

To calculate the speed of the car before the impact, we can use the principle of conservation of mechanical energy. The initial mechanical energy is equal to the final mechanical energy, which is given by the formula:

Initial Mechanical Energy = Final Mechanical Energy

Initial mechanical energy includes the kinetic energy of the car, which is given by:

Kinetic Energy = (1/2) × Mass × Speed²

The final mechanical energy is zero because the car comes to rest. Therefore, we can solve for the speed using the formula:

Speed = √(2 × (Final Mechanical Energy ÷ Mass))